Downloads provided by UsageCountsA nonintrusive proper generalized decomposition scheme with application in biomechanics
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Ferdinando Auricchio; Michele Conti; Xi Zou; Xi Zou; Pedro Díez;
A nonintrusive proper generalized decomposition scheme with application in biomechanics
SummaryProper generalized decomposition (PGD) is often used for multiquery and fast‐response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multiparametric partial differential equations. Most implementations of PGD are intrusive extensions based on in‐house developed FE solvers. In this work, we propose a nonintrusive PGD scheme using off‐the‐shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in‐house flow‐control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two‐ or three‐dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient‐specific simulation.
Engineering, Civil, Engineering, Multidisciplinary, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Numerical analysis--Simulation methods, Mechanics, Mecànica, Engineering (all), :65 Numerical analysis::65Y Computer aspects of numerical algorithms [Classificació AMS], Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica, Engineering, Ocean, :65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations [Classificació AMS], proper generalized decomposition, Numerical Analysi, Engineering, Aerospace, Engineering, Biomedical, Classificació AMS::65 Numerical analysis::65Y Computer aspects of numerical algorithms, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Simulació, Anàlisi numèrica, Classificació AMS::70 Mechanics of particles and systems, :Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica [Àrees temàtiques de la UPC], Applied Mathematics, nonintrusive, simulation and stochastic differential equations, 624, Computer Science, Software Engineering, Engineering, Marine, Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations, 004, Engineering, Manufacturing, Engineering, Mechanical, :Matemàtiques i estadística::Investigació operativa::Simulació [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, model order reduction, Engineering, Industrial, Classificació AMS::65 Numerical analysis::65C Probabilistic methods, :70 Mechanics of particles and systems [Classificació AMS], Numerical analysis
Engineering, Civil, Engineering, Multidisciplinary, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Numerical analysis--Simulation methods, Mechanics, Mecànica, Engineering (all), :65 Numerical analysis::65Y Computer aspects of numerical algorithms [Classificació AMS], Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica, Engineering, Ocean, :65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations [Classificació AMS], proper generalized decomposition, Numerical Analysi, Engineering, Aerospace, Engineering, Biomedical, Classificació AMS::65 Numerical analysis::65Y Computer aspects of numerical algorithms, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Simulació, Anàlisi numèrica, Classificació AMS::70 Mechanics of particles and systems, :Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica [Àrees temàtiques de la UPC], Applied Mathematics, nonintrusive, simulation and stochastic differential equations, 624, Computer Science, Software Engineering, Engineering, Marine, Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations, 004, Engineering, Manufacturing, Engineering, Mechanical, :Matemàtiques i estadística::Investigació operativa::Simulació [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, model order reduction, Engineering, Industrial, Classificació AMS::65 Numerical analysis::65C Probabilistic methods, :70 Mechanics of particles and systems [Classificació AMS], Numerical analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).38 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10% views 62 downloads 67 - 62views67downloads
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These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Influence provided by BIP!impulseImpulse provided by BIP!
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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